A transverse deformation of the form \(w=rg(\theta )\)  is referred to as a conical deformation (with the tip of the cone at \(O\) ). Such deformations appear as solutions in the problems of isolated disclinations [1]}, [2]} and crumpled sheets [3]}, [4]}, [5]}. We establish two results (as two lemmas) in the context of conical deformations and discuss their implications for inextensible (i.e., \(E^e=0\) ) Föppl-von Kármán plate domains with fields having a singular support as a subset of \(\lbrace O\rbrace \)  (hence, \(S = \emptyset \) ). The first is a kinematical result where we seek a general form of the transverse deformation for a compatible bending strain which has a singular support at \(O\)  and a Gaussian curvature which is necessarily trivial outside \(O\) . As an immediate consequence of the result we show that the Gaussian curvature at \(O\)  is a Dirac, and hence dislocation and vacancy like defects are not supported. The second result considers a specific form of the deformation and the stress function and shows that no point force (or couple) can appear at \(O\)  as a result of transverse force equilibrium. The implications of these results on surfaces with an isolated defect and surfaces under constrained deformation will be noted.
